“You can better appreciate the world when you understand the math behind it. Mathematics is powerful to solve problems. Our entire society is based on mathematical tools. If you learn math, you get better at everything.”
Woo’s tips for HSC math
- Just do it
“Math is a practical subject, like music or sports. It doesn’t matter how many times you watch or read such a skill, you just have to do it hundreds and thousands of times to get good at it. Math really rewards the effort and time you put in. If you read this early you will have time for this. It is difficult to develop a conceptual understanding of an idea in mathematics by cramming it.”
- Explain your answer to a friend
“What we judge in mathematics is: Do you understand? Can you explain why your answer is correct? We are looking for you to share your understanding – do you understand? So I suggest going to a friend and explaining the solutions to some questions to him. It will deepen your understanding and compel you to explain.”
- Find and try unfamiliar questions
“By the HSC exams, you’ve learned every topic in math, which means they can ask you anything – but they can also combine these in unusual and non-routine ways. In the HSC exams, the most difficult questions are those that combine multiple subject areas. When you’re revising, the textbook just presents you with questions on a topic—in neat, neat little chapters. It’s good for gradually learning skills, but not for assessing one’s understanding of how this concept can be linked to another.” Trying out previous HSC exam questions can be helpful for practicing answering this type of non-routine question.
- Put yourself under time pressure
“Your brain behaves differently under stress. Using a previous work, I would try to give myself three hours to complete it so I train myself to complete the full work and have time to review it. I didn’t manage to finish on time at first, so I found that the last few questions I didn’t have time to answer were multi-topic and more challenging. So practicing under time pressure helps train the brain.”
- Watch out for small mistakes
“Often we lose a lot of grades and feel silly when it comes to the little questions – the straight A questions. It’s even more important that you go over these little questions once you’ve finished work and double-check your answers, because we run the risk of rushing them. Having detailed lines of elaboration – as opposed to just writing the final answer – is not only useful for communicating with the editor, it’s also helpful when revisiting an answer to follow your own logic and pinpoint potential errors.”
Quality study instead of quantity, says math ace
It might be hard to believe, but Manal Khan – who took the advanced math class at HSC 2020 – showed little interest in math during her elementary school days. It wasn’t until high school that her interest in the subject matched her ability.
“By the time I was in primary school, my mother had given up all hope for my math skills, so you can imagine what a turning point it was in later years,” said Khan, who attended Amity College in western Sydney.
Her recipe for success in this demanding subject was diverse.
“It wasn’t just one thing, it was a combination of many things — the resources I had, my teachers and classmates, the amount of practice I put in, daily habits like sleep schedules, and so on,” she said.
Above all, it was a matter of having the right mentality. “I have always felt that the way you think is a key factor in being successful. You have to be determined and believe that you can actually achieve that goal – and for me, my religion plays a big part in my mindset and motivation.”
Khan found that the quality of study time was more important than quantity, and checklists helped her keep track.
“Some people care a lot about how much time they spend studying, but I’ve always measured my progress by the amount of work I’ve done, not the time I’ve put into something. I also used checklists to keep track of my work and stay organized. Checklists really help when everything seems overwhelming,” she said.
When it came to different issues, Khan adjusted and modified their approach.
“The way I learned differed from subject to subject. For subjects that involve a lot of arithmetic, such as math, I revise the theory behind each topic, but learn mostly by answering actual questions. Mathematics cannot be relied upon to be memorized.
“With other subjects like biology or English, my focus at first was more on understanding the content and not so much on trying out questions until I had a thorough grasp of the concepts,” she said.
Self-care, rest and extracurricular activities also played a big role in her coming through HSC healthy and balanced.
“The hardest part has been staying motivated, especially during the COVID lockdowns. However, going through it with my friends and colleagues definitely helped. As many of us joked, it was a ‘collective experience,'” she said.
After graduating, Khan began studying optometry but has now switched to medicine at UNSW Sydney.
For this top student, it’s all about the attitude you bring to everything you’ve taken on.
“The perspective you have on things makes all the difference. You are free to choose your subjects, so get to know them with interest. After all, you are always working towards something. So do you really want to live your life with stress? Happy learning and good luck!”
Khan’s tips for HSC Maths:
- Meanwhile, do your homework: “That way, as the exams get closer, you can focus more on learning than ‘learning’ the subjects.”
- Do you have an “error document”: “Use this to record common mistakes you make — for example, not checking whether the answer is within the domain.”
- Note the key takeaways: “Create notes to summarize key ideas, formulas, and tips, as well as any challenging questions you come across on your homework or classroom exercises.”
- Do you know your presumed knowledge: “For the HSC and exams, revise formulas from 11th grade that are “assumed knowledge” – things like the sum of angles of polygons.”
- Working with friends: “My colleagues and I have always supported each other in explaining questions and topics. This only strengthens your own understanding and skills.”
Want to learn more about the common content of the Math Standard 2 and Advanced exams? Look at that:
Top tips from an HSC math teacher
Michael Murton, Bowral High School
Member of the New South Wales Government Quality Teaching Practice Unit
To solve an HSC exam problem, look carefully at the information in front of you. Everything you need is there, but proper understanding and interpretation is your key to success.
Here is a question from the Advanced Math exam:
Apply your skills and understanding
For HSC exam problems, plan a strategy based on what you have and where you need to get to, and think about the steps in between. Break the question down in this way, rather than just trying to jump straight to the solution.
To solve the given problems, determine the percentage per period (per month for option 1 and per quarter for option 2) and the corresponding number of periods required. Substitute the appropriate values to find the values for option 1 (using the future value formula on the reference sheet) and option 2 (using the annuity table).
You should also have a reasonable estimate of the values of both investment options as you would expect both answers to be slightly more than the $40,000 invested given the interest rate and time.
Check the plausibility of your answer
Look carefully at your work and assess whether your answer makes sense given the information in the question. It is also important that you read the question again to ensure that you have answered the questions asked. Use a closing statement for your answer. In the given HSC question, a concluding statement might be:
“The difference between Option 1 and Option 2 is $40.87 ($45,097.17 – $45,056.30)”. Ask yourself, “Does that seem reasonable?” And answer the question?”
Most importantly, reread your answers carefully and critically to ensure they make sense for a marker.